Biomedical Engineering Reference
In-Depth Information
Tabl e 4
Deterministic rates
for the 4-phases of
lymphocyte recruitment
Process
k
on
(sec
1
)
k
off
(sec
1
)
Tethering
84
1
Rolling
84
100
Chemokines activation
0.5
75
Firm adesion
84
20
involved in rolling of the cell, so that they undergo an alternate binding/unbindig
with their ligands represented by the processes VCAM1 and ICAM1. For the inter-
action between the ALPHA4 ACTIVE and VCAM1 the implementation follows the
same track of the previous cases of complex formation and breakage. The reaction
between LFA1 ACTIVE and ICAM1 processes leads to the formation of a stable
complex, represented by the “bound” states LFA1 BOUND and ICAM1 BOUND,
implementing the firm adhesion of the lymphocyte.
We simulated the role and the contribution of the different interactions as bi-
molecular binding processes occurring at different rates (Table
4
). The selectins
interaction PSGL1/PSELECTIN plays a crucial role in guaranting an efficient
rolling, therefore the channels rates for the communication in the binding process
between PSGL1 and PSLECTIN have been calculated from the deterministic rates
of the kinetic model, that reproduce the tethering and rolling motion. Analogously,
for the ALPHA4 ACTIVE/VCAM1 interaction, that contributes to rolling and, in
part, also to cell arrest, the channels rate have been calculated from the deterministic
rates that recreate the rolling motion. The interaction LFA1 ACTIVE/ICAM1 is
the main responsible of firm arrest of the cell on the endothelium and thus the
rates of communication between LFA1 ACTIVE and ICAM1 ACTIVE have been
calculated from those reproducing the firm adhesion in mechanic simulations.
The whole process of lymphocyte recruitment occur in a space of V
D
1:96
10
5
m
3
, corresponding to a volume of a vessel of 25 mofradiusand100 mof
length, and in a simulated time of 15 s. In the considered volume V , the number of
molecules is of the order of 10
6
. In our simulations the values of the volume and of
the molecules number have been proportionally re-scaled by this factor, to make the
code computationally faster.
The stochastic reaction rates for bimolecular binding/unbinding reaction are
inversely proportial to the volume of space in that the reactions occur
[
13
], in
particular for the stochastic association rate we have that RA
D
k
on
=V and for
the stochastic dissociation rate we have RD
D
2k
off
=V ,wherethek
i
's are the
deterministic rates.
4R su s
The output of simulation is the time-evolution of number of bonds (shown in
Fig.
2
) assuming the following densities expressed in m
2
: PSGL-1 [
23
]and
P-SELECTIN 5600, ALPHA4 [
5
] and VCAM-1 85, CHEMOREC and CHEMOKI-
NES 15000, LFA-1 [
14
] and ICAM-1 5500.
